Supplementary Material: Data-Efficient Augmentation for Training Neural Networks A Proof of Main Results A.1 Proof for Lemma 4.1 Proof

B.2 Proof of Theorem B.1 Using Jensen's inequality, we have E null null y f (X As in the proof for Theorem 5.2, we begin with the following inequality E[ null L (W Eq. (9), have large singular values. Applying Eq. (66) and Lemma B.4, we obtain null L ( W, X We generate singular spectrum plots for both MNIST and CIFAR10 datasets in Figure 1. AutoAugment include translations, shearing, as well as contrast and brightness transforms. For all experiments, we train using SGD with 0.9 momentum and learning rate decay. D.8, where we train for 400 epochs to ensure convergence with a starting learning rate of For all experiments, we train using SGD with 0.9 momentum and learning rate decay.